Deleted compositing layout -- How to bring it back?
The custom screen layouts are saved in a blend file but they don't show up when we append data from another file. This leaves two choices, recreate the layout that is missing, or open the file without the screen layouts and replace all of the screens in the file.

To create a new screen layout click the + next to the screen list and give it a useful name. Now adjust the layout so that the editors are where you want them and save your blend file.

If you start with a file (maybe your default startup) that has the layouts you want to use, turn off load UI when you open your blend file so you keep the existing layouts, then resave the blend file with these layouts. Not that this removes any cutsom screen layouts you may have had in your file.